面向分布式异构资源分配的AIMD有限平均收敛性
The Convergence of Finite-Averaging of AIMD for Distributed Heterogeneous Resource Allocations
AI总结：
本文针对分布式异构资源分配问题，分析了基于随机化AIMD算法、仅需与中央智能体少量通信的分布式方案，通过有限窗口时间平均和位置依赖概率马尔可夫链建模，证明了时间平均分配向量收敛到唯一不变测度且具有遍历性。
摘要：
在若干社会选择问题中，智能体集体对多种可分割且异构的、具有容量约束的资源分配进行决策，以最大化功利主义社会福利。智能体受到计算资源、通信资源或隐私考虑的限制。本文分析了一种最近提出的分布式解决方案的收敛性，该方案以最少的通信将此类资源分配给智能体。它基于随机化的加法增加与乘法减少（AIMD）算法。智能体之间无需交换信息，只需与一个中央智能体进行少量通信，该中央智能体跟踪某一时刻已分配的聚合资源量。我们对有限窗口大小下的时间平均分配进行建模，并将系统刻画为具有位置依赖概率的马尔可夫链。进一步，我们证明时间平均分配向量收敛到唯一的不变测度，并且遍历性质成立。
英文摘要：
In several social choice problems, agents collectively make decisions over the allocation of multiple divisible and heterogeneous resources with capacity constraints to maximize utilitarian social welfare. The agents are constrained through computational or communication resources or privacy considerations. In this paper, we analyze the convergence of a recently proposed distributed solution that allocates such resources to agents with minimal communication. It is based on the randomized additive-increase and multiplicative-decrease (AIMD) algorithm. The agents are not required to exchange information with each other, but little with a central agent that keeps track of the aggregate resource allocated at a time. We formulate the time-averaged allocations over finite window size and model the system as a Markov chain with place-dependent probabilities. Furthermore, we show that the time-averaged allocations vector converges to a unique invariant measure, and also, the ergodic property holds.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
